A satellite is revolving around a planet in an elliptical orbit. Its closest distance to the planet is R_min and the farthest distance R_max. Its angular velocity when nearest to the planet is $ω$ , then angular velocity when it is farthest from the planet is:

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${(\frac{R_{min}}{R_{max}})}^{2} ω$

${(\frac{R_{min}}{R_{max}})}^{1 / 2}$

$\frac{R_{max}}{R_{min}} ω$

${(\frac{R_{max}}{R_{min}})}^{1 / 2} ω$

answer is B.

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Detailed Solution

From conservation of angular momentum ( $Iω$ = constant)
$\begin{array}{l} {mR}_{min}^{2} ω = {mR}_{max}^{2} ω' \\ ω' = {(\frac{R_{min}}{R_{max}})}^{2} ω \end{array}$

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